Results 241 to 250 of about 10,885,302 (272)

Complex Numbers in Algebra [PDF]

, 1989
The next three chapters revisit the topics of algebra, curves, and functions, observing how they are simplified by the introduction of complex numbers. That’s right: the so-called “complex” numbers actually make things simpler. In the present chapter we see where complex numbers came from (not from quadratic equations, as you might expect, but from ...
openaire   +1 more source

Some of the next articles are maybe not open access.

Related searches:

On the Zeta-Functions of Algebraic Number Fields

, 1947
1. It was proved by E. Artin 1 that if k is an algebraic number field (of finite degree) and K a normal extension field with the icosahedral group as the Galois group with regard to k, then the zeta-function g (s, kc) of k divides the zeta-function g(s ...
R. Brauer
semanticscholar   +1 more source

Algebraic number-fields

1967
We shall need some elementary results about vector-spaces over Q, involving the following concept: Definition 1. Let E be a vector-space of finite dimension over Q. By a Q-lattice in E, we understand a finitely generated subgroup of E which contains a basis of E over Q. Proposition 1.
openaire   +2 more sources

ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS

Mathematics of the USSR-Sbornik, 1985
It is proved that among the numbers , where is algebraic, , and is algebraic of degree , there are no fewer than which are algebraically independent over .Bibliography: 17 titles.
openaire   +2 more sources

Algebraic Numbers and Their Polynomials

1991
Straightedge and compass constructions can he used to produce line segments of various lengths relative to some preassigned unit length. Although the lengths are all real numbers, it turns out that not every real number can be obtained in this way. The lengths which can be constructed are rather special.
Sidney A. Morris, Arthur Jones, Kenneth R. Pearson   +2 more
openaire   +2 more sources

A Development of Associative Algebra and an Algebraic Theory of Numbers, I

Mathematics Magazine, 1952
in which if we denote a particular element by Ck, its immediate successor in this is CkJ, where k denotes a natural number and k' its immediate successor in the set of natural numbers. We then introduced in addition to these symbols the symbol + (called a plus sign); x (called a multiplication sign); and (, called a left parenthesis symbol; and ...
M. W. Weaver, H. S. Vandiver
openaire   +2 more sources

Algebraic Number Theory

1982
In this chapter we shall introduce the concept of an algebraic number field and develop its basic properties. Our treatment will be classical, developing directly only those aspects that will be needed in subsequent chapters. The study of these fields, and their interaction with other branches of mathematics forms a vast area of current research.
Kenneth Ireland, Michael Rosen
openaire   +2 more sources

The Schur group of an algebraic number field

, 1976
If G denotes a finite group and Q the rational field, then the group algebra Q[G] is a direct sum of simple rings, each a full matrix ring over a division ring. One may ask which simple rings arise this way as G is allowed to range over all finite groups.
G. Janusz
semanticscholar   +1 more source

Interval exchange transformations over algebraic number fields: the cubic Arnoux–Yoccoz model

, 2007
We apply methods developed for two-dimensional piecewise isometries to the study of renormalizable interval exchange transformations over an algebraic number field , which lead to dynamics on lattices.
J. Lowenstein, G. Poggiaspalla, Franco Vivaldi   +2 more
semanticscholar   +1 more source

Hypercomplex Numbers: From Algebra to Algebras

2015
The term “algebra” dates back to the ninth century AD, but the subject, referring to the solution of polynomial equations, is roughly four thousand years old. It originated in about 1800 BC, with the Babylonians, who solved linear and quadratic equations much as we do today.
Israel Kleiner, Hardy Grant
openaire   +2 more sources